Experiment:
`1_WSE_floodplain_realistic_uncertainty
Here the experiment with the observational data obtained in the
laboratory,averaging the values of the WSE.
Calibration data
A sample was taken of all measurements shown previously:

Corelation plot of MCMC cooked:

Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2001.0000000 |
2001.000000 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2001.000000 |
2001.000000 |
| Minimum |
107.4760000 |
23.356700 |
1.50000e-06 |
5.350170 |
5.473510 |
7.743410 |
6.253130 |
| Maximum |
130.0730000 |
46.343400 |
1.75630e-03 |
17.402300 |
22.259300 |
30.763900 |
27.444300 |
| Range |
22.5970000 |
22.986700 |
1.75480e-03 |
12.052100 |
16.785800 |
23.020500 |
21.191200 |
| Mean |
120.2120000 |
32.501500 |
2.06800e-04 |
10.045000 |
10.231900 |
15.379100 |
15.357700 |
| Median |
119.6200000 |
32.874100 |
1.71700e-04 |
9.793080 |
10.025000 |
15.268400 |
15.098500 |
| Q10% |
114.0310000 |
26.350600 |
3.29000e-05 |
7.671800 |
7.533980 |
11.570400 |
11.315500 |
| Q25% |
116.5180000 |
28.121200 |
6.60000e-05 |
8.672890 |
8.635640 |
13.172900 |
12.937500 |
| Q75% |
124.5030000 |
36.109800 |
3.06300e-04 |
11.206600 |
11.669000 |
17.080600 |
17.506600 |
| Q90% |
126.5360000 |
38.714200 |
4.31000e-04 |
12.853100 |
13.112000 |
19.466900 |
19.593900 |
| St.Dev. |
4.8327100 |
4.779110 |
1.78100e-04 |
1.971020 |
2.200820 |
3.108970 |
3.275740 |
| Variance |
23.3551000 |
22.839900 |
0.00000e+00 |
3.884940 |
4.843600 |
9.665710 |
10.730500 |
| CV |
0.0402015 |
0.147042 |
8.61514e-01 |
0.196220 |
0.215094 |
0.202156 |
0.213297 |
| Skewness |
0.0730142 |
0.104323 |
2.22869e+00 |
0.635261 |
0.571186 |
0.611240 |
0.543355 |
| Kurtosis |
-0.9667830 |
-0.821106 |
1.15867e+01 |
0.351366 |
0.620198 |
1.211530 |
0.343737 |
| MaxPost |
119.8560000 |
32.305200 |
6.37000e-05 |
10.483900 |
9.980640 |
13.988500 |
15.570500 |
| St.Dev. |
4.83271 |
4.77911 |
0.1781380 |
1.97102 |
2.20082 |
3.10897 |
3.27574 |
| MaxPost |
119.85600 |
32.30520 |
0.0636728 |
10.48390 |
9.98064 |
13.98850 |
15.57050 |
Estimation of the friction coefficients
In the main channel:

Estimation of the friction coefficients
In the floodplain:

Residuals
in terms of WSE

In terms of discharge

Notes:
- High negative corelation between a0_kmin and a0_kmoy. They can be
interchangeable and the result will be the same with a weighting or
factor to compensate.
Main conclusions:
The conclusions are presented before describing the experiments, in
order to highlight the key findings of the study.
In laboratory measurements:
- Water depth measurements presented a discrepancy between
measurements in the main channel and the floodplain. Averaging them
could already introduce some errors during modelling.
- A light backwater wave was observed from downstream to upstream.
Indeed, the hydraulic control is the weir located downstream which is
controlling the flow dynamics.
- The height of the weir is not reported. Therefore, the closest
observed water level was chosen as the downstream boundary condition,
introducing non-negligible errors in the modeling.
Results of experiments:
- High corelations between the friction in the main channel and the
floodplain were detected.
- To reduce this corelation, it is necessary to get more information
about the friction at least from one of them, WSE observation with low
uncertainty to restreint the possible combinations of parameters.
- The method is able to estimate the parameters, but special attention
should be paid to the selection of observational data in order to avoid
very high parametric uncertainties.
- To reproduce the observed WSE, the friction values in either the
main channel or the floodplain must be set to unrealistic levels
according to the literature.
Underlying questions:
The method could identify the friction in the main channel and
the floodplain using a single event in floodplain?
Answer:
1_WSE_floodplain_realistic_uncertainty experiment,
presented previously, shows calibration using a single event in
floodplain lead to estimate a high number of good combinations for
reproducing the observed WSE. So, it is possible but parametric
uncertainty is huge due to the strong negative corelation
How to reduce the corelation between kmin/kmoy ?
Answer: Taking a pseudo-observation of the friction
either in main channel or floodplain with low uncertainty to reduce the
number of combinations of the parameters.
A minimal number of events (2) to identify the friction in the
main channel and floodplain? Should one of the events flow only in the
main channel?
Answer: This experiment must be performed in a
synthetic experiment to conclude about it.
Experiment: 1_WSE_floodplain_null_uncertainty
Reduce the uncertainty in the observational data
Calibration data
A sample was taken of all measurements shown previously:

Corelation plot of MCMC cooked:

Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2001.0000000 |
2001.000000 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2001.000000 |
2001.000000 |
| Minimum |
107.4770000 |
24.728800 |
2.28700e-04 |
5.858510 |
5.162780 |
7.256530 |
8.535670 |
| Maximum |
128.5200000 |
47.267600 |
1.02860e-03 |
19.895200 |
19.534400 |
26.391600 |
25.783100 |
| Range |
21.0430000 |
22.538800 |
7.99900e-04 |
14.036700 |
14.371600 |
19.135100 |
17.247400 |
| Mean |
117.0700000 |
35.709300 |
4.68000e-04 |
10.422800 |
10.340100 |
15.183500 |
15.256800 |
| Median |
116.6180000 |
35.924800 |
4.40500e-04 |
10.168100 |
10.021500 |
15.076100 |
14.853100 |
| Q10% |
111.3130000 |
29.928700 |
3.08800e-04 |
7.961250 |
7.902230 |
11.555500 |
11.659700 |
| Q25% |
114.0760000 |
31.904100 |
3.64800e-04 |
9.012630 |
8.877260 |
13.179400 |
13.159800 |
| Q75% |
120.6260000 |
38.717500 |
5.48300e-04 |
11.564200 |
11.582200 |
17.017600 |
17.146600 |
| Q90% |
122.3280000 |
42.365800 |
6.64100e-04 |
13.277000 |
13.104500 |
18.888700 |
19.327900 |
| St.Dev. |
4.3978600 |
4.729290 |
1.39500e-04 |
2.099750 |
2.128930 |
2.922280 |
3.026050 |
| Variance |
19.3412000 |
22.366200 |
0.00000e+00 |
4.408930 |
4.532330 |
8.539750 |
9.156990 |
| CV |
0.0375661 |
0.132438 |
2.98147e-01 |
0.201457 |
0.205891 |
0.192464 |
0.198341 |
| Skewness |
0.1696110 |
0.105879 |
8.07301e-01 |
0.714238 |
0.737369 |
0.450935 |
0.561829 |
| Kurtosis |
-0.6100620 |
-0.633168 |
4.67690e-01 |
0.821512 |
1.008740 |
0.474089 |
0.139611 |
| MaxPost |
118.9850000 |
33.238100 |
3.34500e-04 |
9.791470 |
9.998730 |
14.983100 |
14.560200 |
| St.Dev. |
4.39786 |
4.72929 |
0.139538 |
2.09975 |
2.12893 |
2.92228 |
3.02605 |
| MaxPost |
118.98500 |
33.23810 |
0.334454 |
9.79147 |
9.99873 |
14.98310 |
14.56020 |
Estimation of the friction coefficients
In the main channel:

Estimation of the friction coefficients
In the floodplain:

Residuals
in terms of WSE

In terms of discharge

Notes:
- From the first case, the uncertainty is already low, thus reducing
the uncertainty in the observational data does not help to break the
corelation between the parameters.
- To assess the identifiability of the parameters, non uncertainty in
observation is considered for the rest of the experiments.
Experiment:
1_WSE_floodplain_1_Kmin_null_uncertainty
Add a single pseudo-observation of the friction in the main channel
with very low uncertainty
Calibration data
The WSE observation is considered without uncertainty as the previous
example. Below the calibration data is shown:
| 1 |
1 |
3.50 |
3420 |
0.1643105 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.00 |
3420 |
0.1616392 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.50 |
3420 |
0.1602367 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
0 |
-9999 |
| 1 |
1 |
7.00 |
3420 |
0.1603004 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
7.50 |
3420 |
0.1590004 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.25 |
3420 |
0.1575192 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.75 |
3420 |
0.1552395 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.50 |
3420 |
0.1543078 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.00 |
3420 |
0.1539768 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
Corelation plot of MCMC cooked:

Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2.00100e+03 |
2001.0000000 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2.00100e+03 |
2001.000000 |
| Minimum |
9.99974e+01 |
52.1071000 |
2.09000e-04 |
5.782940 |
5.750480 |
7.60000e-06 |
7.959880 |
| Maximum |
1.00002e+02 |
63.8039000 |
1.97570e-03 |
18.754200 |
19.024200 |
6.41560e-03 |
25.378100 |
| Range |
4.60000e-03 |
11.6968000 |
1.76670e-03 |
12.971300 |
13.273700 |
6.40800e-03 |
17.418200 |
| Mean |
1.00000e+02 |
59.3397000 |
4.64100e-04 |
10.128900 |
10.344600 |
7.17200e-04 |
15.158400 |
| Median |
1.00000e+02 |
59.3257000 |
4.21200e-04 |
9.874710 |
10.137300 |
4.06800e-04 |
14.991500 |
| Q10% |
1.00000e+02 |
57.8182000 |
3.25900e-04 |
7.646060 |
7.841480 |
1.06200e-04 |
11.398700 |
| Q25% |
1.00000e+02 |
58.6624000 |
3.70100e-04 |
8.614600 |
8.887270 |
2.06400e-04 |
13.211300 |
| Q75% |
1.00000e+02 |
60.0413000 |
5.21700e-04 |
11.302100 |
11.589900 |
8.40100e-04 |
16.985500 |
| Q90% |
1.00000e+02 |
60.8575000 |
6.33300e-04 |
12.911600 |
12.932400 |
1.66080e-03 |
18.978500 |
| St.Dev. |
5.14600e-04 |
1.2504500 |
1.70500e-04 |
2.152070 |
2.137930 |
8.37900e-04 |
2.945500 |
| Variance |
3.00000e-07 |
1.5636100 |
0.00000e+00 |
4.631390 |
4.570740 |
7.00000e-07 |
8.675970 |
| CV |
5.10000e-06 |
0.0210727 |
3.67430e-01 |
0.212468 |
0.206672 |
1.16825e+00 |
0.194314 |
| Skewness |
5.13807e-01 |
-0.6787840 |
3.88415e+00 |
0.788049 |
0.673140 |
2.61497e+00 |
0.368663 |
| Kurtosis |
1.27389e+01 |
4.1952700 |
2.57040e+01 |
0.852897 |
0.802783 |
8.41432e+00 |
0.186513 |
| MaxPost |
1.00000e+02 |
59.6315000 |
3.47900e-04 |
9.850530 |
10.173900 |
2.07500e-04 |
14.566800 |
| St.Dev. |
5.146e-04 |
1.25045 |
0.170512 |
2.15207 |
2.13793 |
0.0008379 |
2.9455 |
| MaxPost |
1.000e+02 |
59.63150 |
0.347862 |
9.85053 |
10.17390 |
0.0002075 |
14.5668 |
Estimation of the friction coefficients
In the main channel:

Estimation of the friction coefficients
In the floodplain:

Residuals
in terms of WSE

In terms of discharge

Notes:
- By forcing a observation very tight in the main channel and keeping
a polynomial degree of 0, indicates that the estimation of the friction
in the main channel is already known before the calibration. In other
words, in a constant longitudinal friction, with a very tight
observation of the fricion coefficient in the main channel or floodplain
reduce the number of parameters to estimate of 1.
- No more corelation is observed but this case is not realistic, as
the friction coefficient in the main channel is not known
accurately.
- By fixing the friction coefficient in the main channel, the
estimation of the friction coefficient in the floodplain can be better
identified
Experiment: 1_WSE_floodplain_several_Kmin
Add several pseudo-observations of the friction in the main channel
with a realistic uncertainty
Calibration data
| 1 |
1 |
3.50 |
3420 |
0.1643105 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
5.00 |
3420 |
0.1616392 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
6.50 |
3420 |
0.1602367 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
7.00 |
3420 |
0.1603004 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
7.50 |
3420 |
0.1590004 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
9.25 |
3420 |
0.1575192 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
11.75 |
3420 |
0.1552395 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
12.50 |
3420 |
0.1543078 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
| 1 |
1 |
13.00 |
3420 |
0.1539768 |
-9999 |
-9999 |
100 |
-9999 |
0 |
-9999 |
-9999 |
3 |
-9999 |
Corelation plot of MCMC cooked:

Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2.00100e+03 |
2001.0000000 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2.00100e+03 |
2001.000000 |
| Minimum |
9.69799e+01 |
51.4427000 |
2.01100e-04 |
4.723730 |
5.544260 |
2.64000e-05 |
7.488510 |
| Maximum |
1.02902e+02 |
67.3106000 |
1.48350e-03 |
21.905700 |
18.814600 |
1.18611e-02 |
28.047800 |
| Range |
5.92210e+00 |
15.8679000 |
1.28240e-03 |
17.182000 |
13.270300 |
1.18347e-02 |
20.559300 |
| Mean |
1.00071e+02 |
59.1494000 |
4.70400e-04 |
10.191200 |
10.183600 |
1.57470e-03 |
15.265000 |
| Median |
1.00066e+02 |
59.1092000 |
4.33100e-04 |
9.885030 |
9.977880 |
9.85900e-04 |
15.013200 |
| Q10% |
9.88757e+01 |
56.4398000 |
3.04300e-04 |
7.597470 |
7.684120 |
2.37900e-04 |
11.680100 |
| Q25% |
9.94580e+01 |
57.9080000 |
3.58700e-04 |
8.524780 |
8.800370 |
5.04400e-04 |
13.165500 |
| Q75% |
1.00756e+02 |
60.5620000 |
5.35600e-04 |
11.540700 |
11.523600 |
1.82330e-03 |
17.117400 |
| Q90% |
1.01242e+02 |
61.8728000 |
6.65200e-04 |
13.106700 |
12.806200 |
3.70820e-03 |
19.204900 |
| St.Dev. |
9.74019e-01 |
2.2025400 |
1.62900e-04 |
2.254560 |
2.015270 |
1.70100e-03 |
3.113380 |
| Variance |
9.48712e-01 |
4.8511700 |
0.00000e+00 |
5.083040 |
4.061320 |
2.90000e-06 |
9.693120 |
| CV |
9.73330e-03 |
0.0372369 |
3.46397e-01 |
0.221227 |
0.197894 |
1.08017e+00 |
0.203956 |
| Skewness |
2.04720e-01 |
-0.1253350 |
1.76786e+00 |
0.838544 |
0.512311 |
2.23643e+00 |
0.556226 |
| Kurtosis |
2.70351e-01 |
0.7538870 |
5.10156e+00 |
1.458950 |
0.551952 |
5.63228e+00 |
0.690285 |
| MaxPost |
1.00066e+02 |
59.3612000 |
3.42000e-04 |
8.753080 |
9.791300 |
5.72200e-04 |
14.862800 |
| St.Dev. |
0.974019 |
2.20254 |
0.162940 |
2.25456 |
2.01527 |
0.0017010 |
3.11338 |
| MaxPost |
100.066000 |
59.36120 |
0.341959 |
8.75308 |
9.79130 |
0.0005722 |
14.86280 |
Estimation of the friction coefficients
In the main channel:

Estimation of the friction coefficients
In the floodplain:

Residuals
in terms of WSE

In terms of discharge

Notes:
- Several pseudo-observations of the friction in the main channel lead
to target a set of combinations of the friction coefficients in the main
channel and the floodplain leading to reproduce the observed WSE.
- The corelation between te parameters is reduced but not completely
removed.
Experiment:
1_WSE_floodplain_1_Kmoy_null_uncertainty
Similar as the second proposal but now the pseudo-observation is
taken in the floodplain
Calibration data
| 1 |
1 |
3.50 |
3420 |
0.1643105 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.00 |
3420 |
0.1616392 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.50 |
3420 |
0.1602367 |
-9999 |
-9999 |
-9999 |
33 |
0 |
-9999 |
-9999 |
-9999 |
0 |
| 1 |
1 |
7.00 |
3420 |
0.1603004 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
7.50 |
3420 |
0.1590004 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.25 |
3420 |
0.1575192 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.75 |
3420 |
0.1552395 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.50 |
3420 |
0.1543078 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.00 |
3420 |
0.1539768 |
-9999 |
-9999 |
-9999 |
-9999 |
0 |
-9999 |
-9999 |
-9999 |
-9999 |
Corelation plot of MCMC cooked:

Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2.00100e+03 |
2.00100e+03 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2001.000000 |
2.00100e+03 |
| Minimum |
1.15792e+02 |
3.29932e+01 |
2.08100e-04 |
5.669440 |
5.187250 |
7.542560 |
1.69000e-05 |
| Maximum |
1.22672e+02 |
3.30102e+01 |
1.33990e-03 |
17.042600 |
20.126400 |
30.747800 |
8.93260e-03 |
| Range |
6.88000e+00 |
1.70000e-02 |
1.13170e-03 |
11.373200 |
14.939200 |
23.205200 |
8.91580e-03 |
| Mean |
1.19351e+02 |
3.30002e+01 |
4.57400e-04 |
9.985180 |
10.344600 |
15.347600 |
9.48900e-04 |
| Median |
1.19345e+02 |
3.30000e+01 |
4.31900e-04 |
9.845290 |
10.207600 |
14.865900 |
6.33100e-04 |
| Q10% |
1.18555e+02 |
3.29997e+01 |
3.09100e-04 |
7.537140 |
7.828650 |
11.550500 |
1.76700e-04 |
| Q25% |
1.18880e+02 |
3.30000e+01 |
3.57000e-04 |
8.619260 |
8.932830 |
12.960900 |
3.17700e-04 |
| Q75% |
1.19792e+02 |
3.30004e+01 |
5.16200e-04 |
11.098300 |
11.668900 |
17.215400 |
1.21600e-03 |
| Q90% |
1.20155e+02 |
3.30008e+01 |
6.24800e-04 |
12.658800 |
12.998300 |
20.202400 |
2.04340e-03 |
| St.Dev. |
6.76636e-01 |
9.15200e-04 |
1.42900e-04 |
1.971730 |
2.031410 |
3.297080 |
9.98300e-04 |
| Variance |
4.57836e-01 |
8.00000e-07 |
0.00000e+00 |
3.887730 |
4.126610 |
10.870700 |
1.00000e-06 |
| CV |
5.66930e-03 |
2.77000e-05 |
3.12305e-01 |
0.197466 |
0.196373 |
0.214826 |
1.05207e+00 |
| Skewness |
1.90669e-02 |
1.87550e-01 |
1.52533e+00 |
0.605765 |
0.473508 |
0.812506 |
2.79451e+00 |
| Kurtosis |
1.30900e+00 |
3.11188e+01 |
3.75694e+00 |
0.461507 |
0.563427 |
1.123140 |
1.12049e+01 |
| MaxPost |
1.19483e+02 |
3.30000e+01 |
3.82300e-04 |
10.050600 |
8.951850 |
14.855300 |
2.04800e-04 |
| St.Dev. |
0.676636 |
9.152e-04 |
0.142855 |
1.97173 |
2.03141 |
3.29708 |
0.0009983 |
| MaxPost |
119.483000 |
3.300e+01 |
0.382287 |
10.05060 |
8.95185 |
14.85530 |
0.0002048 |
Estimation of the friction coefficients
In the main channel:

Estimation of the friction coefficients
In the floodplain:

Residuals
in terms of WSE

In terms of discharge

Notes:
- As in the second proposal, the friction coefficient in the
floodplain is already known before the calibration due to the tight
uncertainty in the pseudo-observation.
- By fixing this parameters, the estimation shows that the model needs
to compensate the friction in the main channel to reproduce the observed
WSE.
- The corelation between the parameters is broken but the uncertainty
on the pseudo-observation is not realistic.